For the Young’s double slit experiment a monochromatic source light is used whose wavelength is $λ$ strikes on the slits, separated by distance $d$ as shown in the figure. In the figure, $n$ is refractive index of medium between slits and screen. Where $n_{0}$ and $k$ are constants. ( $D > > d$ )

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The y co-ordinate of central maxima at any time t is $\frac{D \sin ϕ}{n_{0} + k t}$

The velocity of central maxima at any time t as a function of time t is $\frac{- k D \sin ϕ}{{(n_{0} + k t)}^{2}}$

If a glass plate of small thickness b is placed in front of $S_{1}$ _, its refractive index vary with time so that central maxima is formed at O. $n^{1} = n_{0} + k t + \frac{d \sin ϕ}{b}$

Rate of change of velocity of the central maxima has no meaning as source is at large distance

answer is A, B, C.

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Detailed Solution

$A) S_{1} P - S_{2} P = \frac{d y}{D}$

$Δ x = (n_{0} + k t) \frac{d t}{D} - d \sin ϕ = 0$

For central maxima.
$∴ y = \frac{D \sin ϕ}{n_{0} + k t}$ (y-coordinates of central maximum).
Question Image

$B) \frac{- k D \sin ϕ}{{(n_{0} + k t)}^{2}}$ = velocity of central maximum
(C) For central maxima to be formed at O
$n' (\frac{n}{n'} - 1) b = d \sin ϕ$
Here $n' = n_{0} + k t, n$ =refractive index of plate.
$n = n_{0} + k t + \frac{d \sin ϕ}{b}$